(3x-5)*(8-2x)=0

Solution for (3x-5)*(8-2x)=0 equation:

(3x-5)(8-2x)=0

We add all the numbers together, and all the variables

(3x-5)(-2x+8)=0

We multiply parentheses ..

(-6x^2+24x+10x-40)=0

We get rid of parentheses

-6x^2+24x+10x-40=0

We add all the numbers together, and all the variables

-6x^2+34x-40=0

a = -6; b = 34; c = -40;
Δ = b2-4ac
Δ = 342-4·(-6)·(-40)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-14}{2*-6}=\frac{-48}{-12}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+14}{2*-6}=\frac{-20}{-12}
=1+2/3
$